1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Names
open Constr
(** {5 Derived constructors} *)
(** non-dependent product [t1 -> t2], an alias for
[forall (_:t1), t2]. Beware [t_2] is NOT lifted.
Eg: in context [A:Prop], [A->A] is built by [(mkArrow (mkRel 1) (mkRel 2))]
*)
val mkArrow : types -> Sorts.relevance -> types -> constr
val mkArrowR : types -> types -> constr
(** For an always-relevant domain *)
(** Named version of the functions from [Term]. *)
val mkNamedLambda : Id.t binder_annot -> types -> constr -> constr
val mkNamedLetIn : Id.t binder_annot -> constr -> types -> constr -> constr
val mkNamedProd : Id.t binder_annot -> types -> types -> types
(** Constructs either [(x:t)c] or [[x=b:t]c] *)
val mkProd_or_LetIn : Constr.rel_declaration -> types -> types
val mkProd_wo_LetIn : Constr.rel_declaration -> types -> types
val mkNamedProd_or_LetIn : Constr.named_declaration -> types -> types
val mkNamedProd_wo_LetIn : Constr.named_declaration -> types -> types
(** Constructs either [[x:t]c] or [[x=b:t]c] *)
val mkLambda_or_LetIn : Constr.rel_declaration -> constr -> constr
val mkNamedLambda_or_LetIn : Constr.named_declaration -> constr -> constr
(** {5 Other term constructors. } *)
(** [applist (f,args)] and its variants work as [mkApp] *)
val applist : constr * constr list -> constr
val applistc : constr -> constr list -> constr
val appvect : constr * constr array -> constr
val appvectc : constr -> constr array -> constr
(** [prodn n l b] = [forall (x_1:T_1)...(x_n:T_n), b]
where [l] is [(x_n,T_n)...(x_1,T_1)...]. *)
val prodn : int -> (Name.t binder_annot * constr) list -> constr -> constr
(** [compose_prod l b]
@return [forall (x_1:T_1)...(x_n:T_n), b]
where [l] is [(x_n,T_n)...(x_1,T_1)].
Inverse of [decompose_prod]. *)
val compose_prod : (Name.t binder_annot * constr) list -> constr -> constr
(** [lamn n l b]
@return [fun (x_1:T_1)...(x_n:T_n) => b]
where [l] is [(x_n,T_n)...(x_1,T_1)...]. *)
val lamn : int -> (Name.t binder_annot * constr) list -> constr -> constr
(** [compose_lam l b]
@return [fun (x_1:T_1)...(x_n:T_n) => b]
where [l] is [(x_n,T_n)...(x_1,T_1)].
Inverse of [it_destLam] *)
val compose_lam : (Name.t binder_annot * constr) list -> constr -> constr
(** [to_lambda n l]
@return [fun (x_1:T_1)...(x_n:T_n) => T]
where [l] is [forall (x_1:T_1)...(x_n:T_n), T] *)
val to_lambda : int -> constr -> constr
(** [to_prod n l]
@return [forall (x_1:T_1)...(x_n:T_n), T]
where [l] is [fun (x_1:T_1)...(x_n:T_n) => T] *)
val to_prod : int -> constr -> constr
val it_mkLambda_or_LetIn : constr -> Constr.rel_context -> constr
val it_mkProd_wo_LetIn : types -> Constr.rel_context -> types
val it_mkProd_or_LetIn : types -> Constr.rel_context -> types
(** In [lambda_applist c args], [c] is supposed to have the form
[λΓ.c] with [Γ] without let-in; it returns [c] with the variables
of [Γ] instantiated by [args]. *)
val lambda_applist : constr -> constr list -> constr
val lambda_appvect : constr -> constr array -> constr
(** In [lambda_applist_decls n c args], [c] is supposed to have the
form [λΓ.c] with [Γ] of length [n] and possibly with let-ins; it
returns [c] with the assumptions of [Γ] instantiated by [args] and
the local definitions of [Γ] expanded. *)
val lambda_applist_decls : int -> constr -> constr list -> constr
val lambda_appvect_decls : int -> constr -> constr array -> constr
(** pseudo-reduction rule *)
(** [prod_appvect] [forall (x1:B1;...;xn:Bn), B] [a1...an]
@return [B[a1...an]] *)
val prod_appvect : types -> constr array -> types
val prod_applist : types -> constr list -> types
(** In [prod_appvect_decls n c args], [c] is supposed to have the
form [∀Γ.c] with [Γ] of length [n] and possibly with let-ins; it
returns [c] with the assumptions of [Γ] instantiated by [args] and
the local definitions of [Γ] expanded. *)
val prod_appvect_decls : int -> types -> constr array -> types
val prod_applist_decls : int -> types -> constr list -> types
(** {5 Other term destructors. } *)
(** Transforms a product term {% $ %}(x_1:T_1)..(x_n:T_n)T{% $ %} into the pair
{% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}, where {% $ %}T{% $ %} is not a product. *)
val decompose_prod : constr -> (Name.t binder_annot * constr) list * constr
(** Transforms a lambda term {% $ %}[x_1:T_1]..[x_n:T_n]T{% $ %} into the pair
{% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}, where {% $ %}T{% $ %} is not a lambda. *)
val decompose_lambda : constr -> (Name.t binder_annot * constr) list * constr
(** Given a positive integer n, decompose a product term
{% $ %}(x_1:T_1)..(x_n:T_n)T{% $ %}
into the pair {% $ %}([(xn,Tn);...;(x1,T1)],T){% $ %}.
Raise a user error if not enough products. *)
val decompose_prod_n : int -> constr -> (Name.t binder_annot * constr) list * constr
(** Given a positive integer {% $ %}n{% $ %}, decompose a lambda term
{% $ %}[x_1:T_1]..[x_n:T_n]T{% $ %} into the pair {% $ %}([(x_n,T_n);...;(x_1,T_1)],T){% $ %}.
Raise a user error if not enough lambdas. *)
val decompose_lambda_n : int -> constr -> (Name.t binder_annot * constr) list * constr
(** Extract the premisses and the conclusion of a term of the form
"(xi:Ti) ... (xj:=cj:Tj) ..., T" where T is not a product nor a let *)
val decompose_prod_decls : types -> Constr.rel_context * types
(** Idem with lambda's and let's *)
val decompose_lambda_decls : constr -> Constr.rel_context * constr
(** Idem but extract the first [n] premisses, counting let-ins. *)
val decompose_prod_n_decls : int -> types -> Constr.rel_context * types
(** Idem but extracting simultaneously the first [n] premisses, counting let-ins, in a term and its type. *)
val decompose_lambda_prod_n_decls : int -> constr -> types -> Constr.rel_context * constr * types
(** Idem for lambdas, including let-ins but _not_ counting them;
This is typically the function to use to extract the context of a Fix
up to and including the decreasing argument, counting as many lambda's
as given by the decreasing index + 1 *)
val decompose_lambda_n_assum : int -> constr -> Constr.rel_context * constr
(** Idem, counting let-ins *)
val decompose_lambda_n_decls : int -> constr -> Constr.rel_context * constr
(** Return the premisses/parameters of a type/term (let-in included) *)
val prod_decls : types -> Constr.rel_context
val lambda_decls : constr -> Constr.rel_context
(** Return the first n-th premisses/parameters of a type (let included and counted) *)
val prod_n_decls : int -> types -> Constr.rel_context
(** Return the first n-th premisses/parameters of a term (let included but not counted) *)
val lam_n_assum : int -> constr -> Constr.rel_context
(** Remove the premisses/parameters of a type/term *)
val strip_prod : types -> types
val strip_lam : constr -> constr
(** Remove the first n-th premisses/parameters of a type/term *)
val strip_prod_n : int -> types -> types
val strip_lam_n : int -> constr -> constr
(** Remove the premisses/parameters of a type/term (including let-in) *)
val strip_prod_decls : types -> types
val strip_lambda_decls : constr -> constr
(** {5 ... } *)
(** An "arity" is a term of the form [[x1:T1]...[xn:Tn]s] with [s] a sort.
Such a term can canonically be seen as the pair of a context of types
and of a sort *)
type arity = Constr.rel_context * Sorts.t
(** Build an "arity" from its canonical form *)
val mkArity : arity -> types
(** Destruct an "arity" into its canonical form *)
val destArity : types -> arity
(** Tell if a term has the form of an arity *)
val isArity : types -> bool
(* Deprecated *)
type sorts_family = Sorts.family = InSProp | InProp | InSet | InType | InQSort
[@@ocaml.deprecated "Alias for Sorts.family"]
type sorts = Sorts.t = private
| SProp | Prop | Set
| Type of Univ.Universe.t (** Type *)
| QSort of Sorts.QVar.t * Univ.Universe.t
[@@ocaml.deprecated "Alias for Sorts.t"]
val decompose_prod_assum : types -> Constr.rel_context * types
[@@ocaml.deprecated "Use [decompose_prod_decls] instead."]
val decompose_lam_assum : constr -> Constr.rel_context * constr
[@@ocaml.deprecated "Use [decompose_lambda_decls] instead."]
val decompose_prod_n_assum : int -> types -> Constr.rel_context * types
[@@ocaml.deprecated "Use [decompose_prod_n_decls] instead."]
val prod_assum : types -> Constr.rel_context
[@@ocaml.deprecated "Use [prod_decls] instead."]
val lam_assum : constr -> Constr.rel_context
[@@ocaml.deprecated "Use [lambda_decls] instead."]
val prod_n_assum : int -> types -> Constr.rel_context
[@@ocaml.deprecated "Use [prod_n_decls] instead."]
val strip_prod_assum : types -> types
[@@ocaml.deprecated "Use [strip_prod_decls] instead."]
val strip_lam_assum : constr -> constr
[@@ocaml.deprecated "Use [strip_lambda_decls] instead."]
val decompose_lam : t -> (Name.t binder_annot * t) list * t
[@@ocaml.deprecated "Use [decompose_lambda] instead."]
val decompose_lam_n : int -> t -> (Name.t binder_annot * t) list * t
[@@ocaml.deprecated "Use [decompose_lambda_n] instead."]
val decompose_lam_n_assum : int -> t -> rel_context * t
[@@ocaml.deprecated "Use [decompose_lambda_n_assum] instead."]
val decompose_lam_n_decls : int -> t -> rel_context * t
[@@ocaml.deprecated "Use [decompose_lambda_n_decls] instead."]
|
